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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hardy spaces of vector-valued functions: duality


Author: Oscar Blasco
Journal: Trans. Amer. Math. Soc. 308 (1988), 495-507
MSC: Primary 46E40; Secondary 28B05, 42B30, 46E30
MathSciNet review: 951618
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Abstract: We prove here that the Hardy space of $ B$-valued functions $ {H^1}(B)$ defined by using the conjugate function and the one defined in terms of $ B$-valued atoms do not coincide for a general Banach space. The condition for them to coincide is the UMD property on $ B$. We also characterize the dual space of both spaces, the first one by using $ {B^{\ast}}$-valued distributions and the second one in terms of a new space of vector-valued measures, denoted $ \mathcal{B}\mathcal{M}\mathcal{O}({B^{\ast}})$, which coincides with the classical $ \operatorname{BMO} ({B^{\ast}})$ of functions when $ {B^{\ast}}$ has the RNP.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0951618-8
PII: S 0002-9947(1988)0951618-8
Keywords: Bounded mean oscillation measures, UMD spaces, Radon-Nikodym property, vector-valued atoms
Article copyright: © Copyright 1988 American Mathematical Society